The dependence of galaxy clustering on stellar mass, star-formation rate and redshift at z = 0.8 - 2.2, with HiZELS

The dependence of galaxy clustering on stellar mass, star-formation rate and redshift at z = 0.8 − 2.2, with HiZELS

R. K. Cochrane,

^1?

P. N. Best,

¹

D. Sobral,

^2,3

I. Smail,

⁴

J. E. Geach

⁵

J. P. Stott,

²

D. A. Wake

^6,7

1SUPA, Institute for Astronomy, Royal Observatory Edinburgh, EH9 3HJ, UK 2Department of Physics, Lancaster University, Lancaster, LA1 4YB

3Leiden Observatory, Leiden University, P.O. Box 9513, NL-2300 RA Leiden, The Netherlands

4Centre for Extragalactic Astronomy, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK

5Centre for Astrophysics Research, Science & Technology Research Institute, University of Hertfordshire, Hatfield, AL10 9AB, UK 6Department of Physics, University of North Carolina Asheville, One University Heights, Asheville, NC 28804, USA.

7Department of Physical Sciences, The Open University, Milton Keynes MK7 6AA, UK

Accepted 2017 December 18. Received 2017 December 11; in original form 2017 September 21

ABSTRACT

The deep, near-infrared narrow-band survey HiZELS has yielded robust sam- ples of Hα-emitting star-forming galaxies within narrow redshift slices at z= 0.8, 1.47 and 2.23. In this paper, we distinguish the stellar mass and star-formation rate (SFR) dependence of the clustering of these galaxies. At high stellar masses (M∗/M& 2 × 10¹⁰), where HiZELS selects galaxies close to the so-called star-forming main sequence, the clustering strength is observed to increase strongly with stellar mass (in line with the results of previous studies of mass-selected galaxy samples) and also with SFR. These two dependencies are shown to hold independently. At lower stellar masses, however, where HiZELS probes high specific SFR galaxies, there is little or no dependence of the clustering strength on stellar mass, but the dependence on SFR remains: high-SFR low-mass galaxies are found in more massive dark matter haloes than their lower SFR counterparts. We argue that this is due to environmentally driven star formation in these systems. We apply the same selection criteria to the EAGLE cosmological hydrodynamical simulations. We find that, in EAGLE, the high-SFR low-mass galaxies are central galaxies in more massive dark matter haloes, in which the high SFRs are driven by a (halo-driven) increased gas content.

Key words: galaxies: evolution – galaxies: high-redshift – galaxies: halo – cosmology:

large-scale structure of Universe

1 INTRODUCTION

A rich array of work reveals that key observable galaxy properties including stellar mass, colour, star-formation rate, and morphology correlate with galaxy environments (Butcher & Oemler 1978;Dressler 1980;Baldry et al. 2006;

Peng et al. 2010;Koyama et al. 2013b; Scoville et al. 2013;

Darvish et al. 2016), with massive, red, quiescent spheroids residing in the densest environments. Studies of galaxy en- vironments can help constrain galaxy formation and evolu-

? E-mail: rcoch@roe.ac.uk

tion processes (e.g.Peng et al. 2010). Yet quantifying galaxy environments on a galaxy-by-galaxy basis can be difficult, particularly at high redshifts, because the accuracy of such measurements is highly dependent on the depth and unifor- mity of the observations and the quality of the redshifts (e.g.

Cooper et al. 2005).

The two-point correlation function, which quantifies the clustering strength of a population of galaxies, provides a fairly robust technique for identifying the typical dark mat- ter halo environments of galaxy populations. On large scales, the two-point correlation function is dominated by the linear

‘two-halo term’, which depends on the clustering of galax-

© 2018 The Authors

arXiv:1801.04933v1 [astro-ph.GA] 15 Jan 2018

ies within different dark matter haloes. The two-halo term essentially measures the galaxy bias, a measure of the differ- ence between the spatial distribution of galaxies and that of the underlying dark matter distribution. On small scales, the non-linear ‘one-halo term’, which quantifies the clus- tering of galaxies within the same dark matter halo, domi- nates. Given an understanding of the way in which haloes of different mass cluster (which is reasonably well understood from N-body simulations within the cosmological model, e.g.

Bond et al. 1991; Lacey & Cole 1994; Jenkins et al. 2001), the observed (projected or angular) two-point correlation function enables us to derive the halo occupation of samples of galaxies from their observed clustering. This technique is known as Halo Occupation Distribution (HOD; Ma & Fry 2000; Peacock & Smith 2000; Berlind & Weinberg 2002;

Cooray & Sheth 2002;Kravtsov et al. 2004) modelling. The HOD framework then provides typical host dark mat- ter halo masses for galaxy samples. It is also possible to derive estimates of central and satellite galaxy fractions from the small-scale ‘one-halo term’ (e.g.Zheng et al. 2005;

Tinker & Wetzel 2010).

Galaxy clustering measures provide a statistical de- scription for a population of galaxies rather than quan- tifying environments on a galaxy-by-galaxy basis. Strong trends in clustering strength have been observed with galaxy morphological type (Davis & Geller 1976), colour (Zehavi et al. 2005; Coil et al. 2008; Simon et al. 2009;

Hartley et al. 2010;Zehavi et al. 2011), star-formation rate (Williams et al. 2009; Dolley et al. 2014; Wilkinson et al.

2017) and stellar mass (Wake et al. 2011;McCracken et al.

2015; Coupon et al. 2015; Hatfield et al. 2016), with the more recent studies reaching back to z ∼ 2 − 3. A limited number of studies of Lyman break galaxies have probed even further, back to z ∼ 6 − 7 (e.g. Harikane et al. 2016, 2017; Hatfield et al. 2017). The largest samples have per- mitted the splitting of galaxy populations by more than one observed property. For example,Norberg et al.(2002), using low-redshift (z < 0.15) data from the 2dF survey (Cole et al.

2000), found that both early- and late-type galaxies display higher r₀values and therefore stronger clustering at brighter B-band absolute magnitudes (M_B).Coil et al.(2008) found broadly consistent results at z ∼ 1 using the DEEP2 galaxy redshift survey (Newman et al. 2012), also confirming that at fixed M_B, red galaxies are more strongly clustered than blue galaxies.

Splitting by multiple variables in this manner is im- portant for galaxy evolution studies. A natural consequence of the apparent tight (∼ 0.4 dex scatter) correlation be- tween stellar mass and star-formation rate of star-forming galaxies (the ‘main sequence’, e.g.Brinchmann et al. 2004;

Daddi et al. 2007; Elbaz et al. 2007; Karim et al. 2011) is that fundamental trends in one of these properties manifest as trends in the other. Galaxies with star-formation rates be- low the main sequence can also complicate observed trends:

the fraction of galaxies that are passive increases towards higher stellar masses (Peng et al. 2010;Sobral et al. 2011), and this can give rise to trends with stellar mass which might not exist for the star-forming population only (e.g. the bend- ing of the main sequence,Lee et al. 2015). Therefore, in this work, we aim to investigate the dependence of galaxy clus- tering on galaxy stellar mass and star-formation rate sepa- rately.

The High-Redshift(Z) Emission Line Survey (HiZELS, Sobral et al. 2013a; see Section 2) identifies galaxies via their emission lines, yielding reliably-selected samples of Hα emitters within narrow redshift slices back to z = 2.2. Hα (rest-frame wavelength 6562.8) is the brightest of the hy- drogen recombination lines, which trace the young mas- sive stellar population. Given that Hα is sensitive to star formation on short time-scales (∼ 10⁷yr) and is also well- calibrated and less strongly extincted by dust than ultravio- let light (Garn et al. 2010), it is often used as a tracer of star- formation. The Hα line is red-shifted out of the optical and into the near-infrared at z ∼ 0.5, making it ideal for prob- ing star-forming galaxies at high redshift using wide-field near-infrared ground-based telescopes (e.g.Moorwood et al.

2000; Geach et al. 2008; Koyama et al. 2010, 2011, 2013a;

Lee et al. 2012). The well-defined redshift distributions of the HiZELS samples of Hα-selected star-forming galaxies are ideal for studies of galaxy clustering, and the large numbers of emitters allows for the study of the population divided into many subsamples.

Sobral et al. (2010) presented the first study of Hα luminosity-binned HiZELS galaxies and found evidence of higher clustering strengths for the strongest emitters at z = 0.84. Geach et al. (2008) andGeach et al. (2012) per- formed the first clustering studies of L_Hα-selected galax- ies at z = 2.23, though the sample size was insufficient to split by luminosity. In our previous paper (Cochrane et al.

2017, hereafter referred to as C17), we confirmed that the trends found bySobral et al.(2010) hold to higher redshifts, using larger HiZELS samples at z = 0.8, z = 1.47 and z = 2.23. Transforming clustering strengths to dark mat- ter halo masses using HOD modelling, we found that halo mass increases broadly linearly with L_Hα at all three red- shifts. Scaling by the characteristic ‘break’ of the Hα lumi- nosity function, L^∗

Hα, transforms these relations to a single trend, revealing a broadly redshift-independent monotonic relationship between L_Hα/L^∗

Hα and halo mass (Sobral et al.

2010; see also Khostovan et al. 2017 for similar relations with other line emitters). For all of our samples, L^∗_Hαgalax- ies reside in dark matter haloes of mass ∼ 10¹²M, the known peak of the stellar mass - halo mass relation (e.g.

Behroozi et al. 2010). We also found low satellite fractions (∼ 5%) for these samples. This suggested that the star- formation rates of central galaxies are being driven by the mass accretion rates of their dark matter haloes (see also Rodr´ıguez-Puebla et al. 2016, for details of a stellar-halo ac- cretion rate coevolution model that matches observational data well).

Sobral et al. (2010) used the K-band luminosities of HiZELS galaxies as a proxy for their stellar mass, finding an increase in galaxy clustering with increasing K-band lu- minosity, though the trend was significantly shallower than was observed for Hα luminosities. Preliminary investigations in C17 involved splitting our larger sample of galaxies at z = 0.8 into two bins by observed K-band magnitude. In- triguingly, we found that the strong, roughly linear rela- tionship between log₁₀L_Hα and r₀ held for our two sam- ples, with any differences between the two K-band magni- tude bins being much smaller than the trend with Hα lumi- nosity.Khostovan et al.(2017) present consistent results in their study of Hβ+ [OII] and [OIII] emitters from HiZELS:

clustering strength increases more significantly with emis-

Hα emitters

NBJ (COSMOS & UDS) 0.845 ± 0.011 503

NBJ (SA22) 0.81 ± 0.011 2332

NBH (COSMOS & UDS) 1.47 ± 0.016 451 NBK (COSMOS & UDS) 2.23 ± 0.016 727 Table 1. Numbers and mean redshifts of Hα emitters identified by the HiZELS survey and selected for this analysis (Sobral et al.

2013a,2015). Only emitters which exceed the limiting flux, f50, of their frames are included in this work.

sion line strength than with galaxy stellar mass.

In this paper, we extend our previous work to study the clustering of HiZELS star-forming galaxies as a function of both Hα luminosity and stellar mass in more detail. Rather than using K-band observed magnitude as a proxy for stellar mass, we use a full SED-fitting approach to estimate stellar masses. We then compare our observational results to the output of the state-of-the-art cosmological hydrodynamical simulation EAGLE (Crain et al. 2015;McAlpine et al. 2015;

Schaye et al. 2015). The structure of this paper is as follows.

In Section2we provide a brief overview of the HiZELS sur- vey and discuss our stellar mass estimates in some depth.

In Section3we review the clustering and HOD-fitting tech- niques presented in C17 that we adopt here. In Section4we present our results, and in Section5we compare these to the output of the EAGLE simulation. Conclusions are drawn in Section6.

We use an H₀= 70kms⁻¹Mpc⁻¹, Ω_M= 0.3 and ΩΛ= 0.7 cosmology throughout this paper.

2 THE HIZELS SURVEY AND SAMPLE

SELECTION

2.1 Samples of Hα emitters

Our sources are drawn from HiZELS, selected by their emis- sion line strength as detailed in Sobral et al. (2013a) and Sobral et al.(2015). A combination of narrow- and broad- band images are used to identify Hα emitters, yielding sources within narrow redshift ranges (∆z ∼ 0.02) centred on z = 0.81 & 0.84 (hereafter z = 0.8), z = 1.47, z = 2.23.

The galaxies used in this paper are the same as those used by C17: we impose the criterion that sources exceed f₅₀, the 50% completeness flux of their survey frames. Raw Hα narrow-band fluxes are corrected for dust extinction by 0.4 dex (A_Hα= 1). An equivalent width-dependent [NII] line contamination correction is made to account for emission from the [NII]6548, 6584 lines that also fall into the narrow- band filter (seeSobral et al. 2013a). Star-formation rates are derived directly from dust-corrected Hα luminosities, L_Hα using

SFR_Hα(Myear⁻¹)= 4.6 × 10⁻⁴²L_Hα(ergs s⁻¹), (1) adopting the calibration ofKennicutt(1998) and scaling by a factor 1.7 (Speagle et al. 2014) to convert from aSalpeter (1955) IMF to aChabrier(2003) IMF.

2.2 Deriving stellar masses from deep broad-band imaging

In order to estimate stellar mass, we model each galaxy’s stellar populations and dust content via spectral energy distribution (SED) fitting using a similar method to that described in Sobral et al. (2011) and Sobral et al. (2014).

The observed photometry is first shifted into the rest-frame.

Model galaxy SEDs are then convolved with the detector’s spectral response function to compare modelled and ob- served flux, and fitted via χ² minimization.

Our modelling draws upon the stellar population synthesis package of Bruzual & Charlot (2003), using the updated models commonly referred to as CB07. These models assume aChabrier(2003) IMF and an exponentially declining star-formation history of the form e^−t/τ, whereτ is in the range 0.1 − 10Gyr. Although this is not a realistic description of the star-formation histories of individual galaxies, which are likely to be characterized by shorter bursts, triggered by stochastic accretion,τ is a reasonable estimate of the mean age of a galaxy (see alsoSobral et al.

2014, who show that using single exponential star-formation models does not introduce any significant bias into the stellar mass estimates of HiZELS galaxies). We use a grid of ages from 30Myr to the age of the Universe at each redshift, with a grid of dust extinctions from Calzetti et al. (2000) up to E(B − V)= 0.5, and three metallicities (0.2 − 1.0Z).

For the COSMOS field, up to 36 wide, medium and narrow bands are used, from GALEX’s far-UV band to Spitzer’s four IRAC bands. In the UDS field there are only 16 available bands, but J, H and K data from UKIRT/UKIDSS DR5 are very deep. Seven bands (ugrizJK) are used in SA22 (seeSobral et al. 2013b). All HiZELS sources are assumed to lie at the central wavelength of the redshift distribution, which is a reasonable approximation since the filter profile is extremely narrow (see Table 1). The resultant stellar masses are fairly well constrained, with typical statistical uncertainties of 0.23, 0.24 and 0.26 dex at z= 0.8, 1.47 and 2.23, which vary a little from source to source. SED masses are plotted against Hα luminosities for the HiZELS samples in Figure 1. At each redshift, our samples cover a very wide range in stellar mass (10⁸ < M∗/M < 10¹¹) and also around 1 dex in Hα luminosity, spanning the break of the luminosity function.

As a test of our stellar masses, especially in SA22, where fewer bands are available, we compare our stellar mass estimates to apparent K-band luminosities, which broadly trace the older stellar population (e.g.Kauffmann 1998; Longhetti & Saracco 2009). Figure 2 shows SED- derived stellar mass versus observed K-band magnitude for HiZELS galaxies in the SA22 field at z= 0.8. These galaxies occupy a clear locus in this plane, close to the line expected from direct proportionality between K-band flux (rest-frame 1.2µm) and stellar mass. At fixed K-band magnitude, redder galaxies (see colour coding) have higher SED masses than would be expected from a naive extrapolation of K-band flux, and bluer galaxies have lower derived SED masses.

This is exactly as expected, since the red fraction is higher for higher luminosity sources. These galaxies are dominated by old stars and have high mass-to-light ratios. In contrast, the bluer (typically less luminous) galaxies in our HiZELS samples have younger stellar populations, and are thus

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z= 0.8

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Figure 1. Distributions of SED-estimated stellar masses and dust-corrected Hα luminosities for the three samples of HiZELS galaxies, at z= 0.8, z = 1.47 and z = 2.23. The dashed lines show LHα^∗ at each redshift, derived bySobral et al.(2013a) andCochrane et al.(2017).

Overplotted are indicative regions of the ‘main sequence’ at each redshift with 2σ contours, derived bySpeagle et al.(2014).

particularly luminous for their mass. We conclude that our SED masses are reasonable, and fold in important colour information. Therefore, we use the SED-derived stellar masses for the remainder of this paper, with confidence.

We note, nevertheless, that our results are qualitatively unchanged whether we use K-band-derived or SED-derived masses.

3 QUANTIFYING GALAXY CLUSTERING

USING THE TWO-POINT CORRELATION FUNCTION

We quantify the clustering of subsamples of HiZELS galaxies using the same techniques as C17, and the interested reader should refer to that paper for more details. Here, we provide a brief overview of our methods.

3.1 Angular two-point clustering statistics

The angular two-point correlation function, w(θ), is defined as the excess probability of finding a pair of galaxies sepa- rated by a given angular distance, relative to that probability for a uniform (unclustered) distribution with the same areal coverage. The probability dP(θ) of finding galaxies in solid angles dΩ₁ and dΩ₂ is thus dP(θ) = N²(1+ w(θ)) dΩ1dΩ₂, where N is the surface density of galaxies. w(θ) is generally calculated by comparing the distribution of sources to that of a randomly distributed population subject to the same sample selection criteria. We use random samples of galax- ies as described in C17. Random galaxies have luminosities drawn from the luminosity function constructed from the same samples, not exceeding the limiting flux of their simu- lated detection frame, and taking into account the effects of incompleteness and flux boosting.

Following C17, we use the minimum variance estimator proposed byLandy & Szalay(1993), which was shown to be minimally susceptible to bias from small sample sizes and

19 20 21 22 23 24 25 26 K

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0 1 2 3

r − J

Figure 2. SED-derived stellar mass versus observed K-band mag- nitude for SA22 galaxies, colour-coded by r − J colour. The black line shows the direct proportionality between K-band flux (rest- frame 1.2µm) and stellar mass (i.e. gradient fixed at −0.4). The stellar mass is clearly well correlated with K-band flux, but at fixed K-band magnitude, redder galaxies have higher SED-derived stellar masses, as would be expected. This colour dependence ap- pears to drive the scatter in the relation and the deviation of the points from the straight line shown.

fields:

w(θ) = 1 + N_R N_D

2 DD(θ) RR(θ) − 2N_R

N_D DR(θ)

RR(θ). (2)

N_Rand N_Dare the total number of random and data galax- ies in the sample, and RR(θ), DD(θ), and DR(θ) correspond to the number of random-random, data-data, and data-random pairs separated by angle θ. w(θ) is normally fitted with a power-law, w(θ) = Aθ^−0.8.

We estimate uncertainty using the bootstrap resam- pling method, with the HiZELS observed frames forming our resampled volumes. Each correlation function was con- structed from 1000 bootstraps, taking the error on each

10 ¹ 10 ² 10 ³ θ/ arcsec

10 ^-2 10 ^-1 10 ⁰ 10 ¹

w ( θ )

HiZELS data HOD fit power-law fit

1 2 3 4 5 6 7 8 9 r ₀ /h

⁻

¹ Mpc

10 ¹¹ 10 ¹² 10 ¹³

M ha lo /M

¯

z = 0 . 8 M _eff

M min

Figure 3. Left: The two-point angular correlation function constructed for the whole sample at z = 0.8, fitted with a power-law (r0= 2.58^+0.16_−0.14h⁻¹Mpc) and HOD model (Meff= 12.13^+0.10_−0.09M). Right: r0− Mhalocalibration fromCochrane et al.(2017). Overplotted are the best-fitting relations log₁₀Meff/M= 11.7 ± 0.7 + r0/(4.5 ± 0.3) and log₁₀Mmin/M= 10.9 ± 0.7 + r0/(4.5 ± 0.3). We find excellent linear fits, so use r0as a proxy for halo mass in this paper.

w(θ) bin as the diagonal element of the bootstrap covari- ance matrix. These uncertainties are quite conservative (see Norberg et al. 2009), enhanced by variations between frames of different depths. As described in C17, we make a small correction, the integral constraint (Groth & Peebles 1977), to account for the underestimation of clustering strength due to the finite area surveyed.

3.2 Obtaining a real-space correlation length In order to compare the clustering strengths of populations of star-forming galaxies at different redshifts quantitatively, we convert the angular correlation function to a spatial one.

This conversion is often performed using Limber’s approxi- mation (Limber 1953), which assumes that spatial correla- tions that followξ = (r/r0)^γare projected as angular correla- tion functions with slopes β = γ + 1. This simple power-law fit is not reliable for our samples of galaxies, which span fields with separations of degrees and use very narrow fil- ters, meaning that on large scales, the angular separation directly traces the real-space separation (resulting in a slope β = γ on large scales). Therefore, we perform a numerical integration of the exact equation:

w_model(θ) = ψ⁻¹∫ _+∞

0

∫ 2s s√

2φ

2 f_s(s − ∆) f_s(s+ ∆)

R^−γ−1r₀^γ∆ dRds. (3)

Here,ψ = 1 + cos θ, φ = 1 − cos θ, ∆ =p

(R²− 2s²φ)/2ψ, and f_s is the profile of the filter, fitted as a Gaussian profile with µ and σ that depend on the filter being considered (see C17 for the parameters of our filters). We assume the standard value of γ = −1.8. χ² fitting of observed against modelled w(θ), generated using different r₀values, allows us to estimate r₀ and its error (seeSobral et al. 2010).

3.3 Halo Occupation Distribution fitting to obtain halo masses

In C17, we used Halo Occupation Distribution (HOD) mod- elling to derive typical dark matter halo masses for Hα luminosity-binned samples of HiZELS galaxies. HOD mod- elling involves parametrizing the number of galaxies per halo as a function of dark matter halo mass, hN |Mi. Given a set of HOD parameters, a halo mass function and halo bias (here both are adopted fromTinker et al. 2010) and a halo profile (we use NFW; Navarro et al. 1996) we generate a real-space correlation function. For each parameter instance, we simulate the projection of this real-space correlation function and compare the result to our observed two-point correlation functions. We use Markov chain Monte Carlo (MCMC) techniques, implemented using theEMCEEpack- age (Foreman-Mackey et al. 2013), to determine the best- fitting parameters. All fitting is performed using the HMF and HALOMOD packages provided byMurray et al.(2013).

Satellite galaxies are parametrized to have a power-law occupancy above some halo mass, in line with most HOD models. The HOD parametrization of centrals differs from those formulated for mass-limited samples, because although all massive haloes will contain a central galaxy, this need not fall within a star-formation rate limited sample. Recent work byGonzalez-Perez et al. (2018) supports adopting an alternative parametrization for star-forming galaxies, which includes a Gaussian peak for low-mass haloes. Thus, follow- ingGeach et al.(2012) and C17, we parametrize the number of central and satellite galaxies separately as:

hN_cen|Mi= F^Bc(1 − F^A_c)exp

"

−log(M/M_min)² 2(σ_{log M})²

#

+1 2F_c^A

"

1+ erf log(M/M_min) σ_{log M}

! # ,

(4)

hN_sat|Mi= Fs

"

1+ erf log(M/M_min) σ_{log M}

! # M M_min

!α

. (5)

The key parameters are:

– M_min: the minimum halo mass that hosts a galaxy. Note that our definition differs subtly to that used in work char- acterizing mass-limited samples, such asMcCracken et al.

(2015) andHatfield et al.(2016), since in this work M_min applies to both central and satellite galaxies.

– σ_{log M}: characterises the width of the transition to hN_sat| Mi= Fs

 M Mmin

α

around M_min.

– α: the slope of the power-law for hNsat| Mi in haloes with M > M_min. In line with the literature, we fixα = 1. Tests al- lowingα to vary confirm that this is an appropriate choice.

– F_c^{A, B}: normalization factors, in range [0,1].

– F_s: the mean number of satellite galaxies per halo, at M= Mmin

The total number of galaxies is given by:

hN |Mi= hNcen| Mi+ hNsat| Mi. (6) When fitting the models to data, we use the observed num- ber density of galaxies as an additional constraint. For a given hN |Mi output from the halo model, the predicted num- ber density of galaxies is:

n_g=

∫

dMn(M)hN | Mi, (7)

where n(M) is the halo mass function, for which we use the determination ofTinker et al.(2010). The observed number density of galaxies used here is the integral of the luminosity function between the same limits used to select the real and random galaxy sample.

For each set of HOD parameters, we may derive a num- ber of parameters of interest for galaxy evolution. In this paper, we use the effective halo mass, the typical mass of galaxy host halo. This is given by:

M_eff= 1 ng

∫

dM Mn(M)hN | Mi. (8)

3.4 Calibrating r₀ to M_halousing HOD models For samples of galaxies with large satellite fractions, there will be a substantial one-halo term in the correlation func- tion at small separations. In such cases, HOD modelling of- fers a better fit than a simple power-law. In C17, we found that HiZELS samples at z= 0.8, z = 1.47 and z = 2.23 have low satellite fractions (∼ 5%), and HOD fitting offers only marginal gains in goodness of fit at small scales (see Figure 3, left-hand panel). Instead, the main benefit of HOD fitting is to allow the conversion of clustering strengths into typical halo masses. Comparing measured r₀to derived halo masses (Figure 3, right-hand panel), we find that these are tightly correlated, and can be reasonably approximated as simple linear fits. At z= 0.8, these are given by:

log₁₀M_eff/M= 11.7 ± 0.7 + r0/(4.5 ± 0.3) (9)

log₁₀Mmin/M= 10.9 ± 0.7 + r0/(4.5 ± 0.3). (10)

Therefore, in some parts of this paper (Section 4.1- 4.4), we simply derive and quote r₀ values, as these are sufficient to indicate trends of clustering with stellar mass or star- formation rate. When we require robust halo masses, as in Sections4.5and5, we perform the full HOD fitting.

4 CLUSTERING OF HIZELS GALAXIES AS A

FUNCTION OF STELLAR MASS AND SFR 4.1 Clustering as a function of Hα luminosity In C17, we studied the clustering of HiZELS galaxies as a function of their Hα luminosity. We found strong relation- ships between L_Hαand r₀. The clustering strength increases monotonically with Hα luminosity at all redshifts, indicating that the most highly star-forming galaxies thrive in higher dark matter overdensities (see Figure4). We speculated that this is where a plentiful gas supply fuels high star-formation rates.

HOD fitting revealed that typical Hα-emitting galaxies are star-forming centrals, residing in host haloes with mini- mum mass increasing with Hα luminosity from ∼ 10^11.2M

to ∼ 10^12.6M and corresponding effective halo masses ∼ 10^11.6M− 10¹³M. At all three redshifts, L_Hα^∗ galaxies typ- ically reside in haloes of effective mass ∼ 10¹²M. This co- incides with the halo mass predicted by theory to be maxi- mally efficient at converting baryons into stars. Samples se- lected within the same L_Hα/L^∗_Hαrange inhabit similar pop- ulations of dark matter haloes. The relationship between scaled galaxy luminosity L_Hα/L_Hα^∗ and dark matter halo mass is largely independent of redshift.

4.2 Clustering as a function of stellar mass

C17 briefly looked at K-band observed luminosities. We found that the trends in clustering strength with L_Hα do not differ between two large K-band bins, concluding that they are unlikely to be driven by stellar mass. Here, we ex- tend that study to provide a more definitive answer to the role stellar mass plays.

Initially we bin our sample of z ∼ 0.8 HiZELS galaxies by stellar mass, construct correlation functions and fit these as described in Section3.1, obtaining a clustering strength r₀ for each subsample. We use the broad bins in Hα luminosity as defined by C17 (−0.4 < log₁₀(L_Hα/L^∗

Hα) < 0.3) for con- sistency, but find no significant differences when we re-run the analysis with no luminosity cuts except for the HiZELS selection. We find that the clustering strength is broadly constant with stellar mass at low galaxy masses. This is particularly clear at z= 0.8, where our samples are largest and probe lowest in stellar mass, but all three redshifts are consistent with this result. The clustering strength only in- creases when we reach stellar mass bins that contain a sig- nificant number of galaxies below the main sequence: at all three HiZELS redshifts, clustering strength increases signif- icantly above a mass 2 − 3 × 10¹⁰M and the most massive galaxies are very strongly clustered (see Figure4 and Ta- ble2). For our Hα-selected samples, the M∗− r₀ relationship appears substantially weaker than the L_Hα− r₀ relation ob- tained by C17, and shown in Figure4for comparison, which continues to decrease at low Hα luminosities.

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Figure 4. Top: clustering strength, r0, as a function of stellar mass. At all three redshifts, the clustering strength is broadly flat at low stellar masses, with evidence for an increase for the most massive galaxies (above ∼ 2 − 3 × 10¹⁰M). Bottom: r0versus LHα from C17, replotted for comparison. Here, a strong monotonic trend is seen between r0and LHαat z= 0.8 and z = 2.2; as shown in C17, the z = 1.47 data are consistent with the same trend (albeit noisier due to the smaller sample).

Whilst the gradient of the stellar mass - halo mass relation of mass-selected galaxies does decrease below M∗ ∼ 10¹⁰M (see Section 4.5; Moster et al. 2010, 2013;

Behroozi et al. 2013 and many others), the flattening we observe for these Hα-selected galaxies is very pronounced.

This indicates that low-mass HiZELS galaxies reside in more massive dark matter haloes than would be expected for star- forming central galaxies of these stellar masses. Although this might be surprising, given that C17 found low satel- lite fractions for these samples, it is important to remember that, at these masses, HiZELS Hα-selected galaxies lie well above the ‘main sequence’. We explore the joint dependence of clustering on both stellar mass and L_Hα in the following subsection.

4.3 Splitting by both stellar mass and Hα luminosity

Within the star-forming population, higher mass galaxies tend to have higher star-formation rates (and therefore higher Hα luminosities), so trends in mass can manifest as apparent trends in star-formation rate, and vice-versa. Here,

r₀ increases significantly at both high L_Hα and high stellar masses, and it is hard to tell the extent to which mass and lu- minosity are each independently correlated with halo mass.

Our large samples of HiZELS galaxies allow us to break this degeneracy, and study trends in stellar mass and L_Hα lumi- nosity independently.

At z = 0.8, where our sample is largest, we split the stellar mass - L_Hαplane into ∼ 500 overlapping subsamples, constructing and fitting two-point correlation functions for each. In Figure5, we present a 2D plot of stellar mass versus L_Hα. Each region is colour-coded by its r₀ value, obtained via a smoothed grid using x and y values of each subsam- ple’s mean stellar mass and star-formation rate, respectively.

Note that these r₀ measurements are not independent, due to the overlapping samples. With around 100 galaxies per bin, there are approximately 30 independent subsamples.

We find that clustering strength increases broadly monoton- ically with L_Hα at all stellar masses. At high stellar masses M∗≥ 10¹⁰M, r₀also increases with stellar mass, as has been found by many mass-selected clustering studies. At low stel- lar masses, the stellar mass-r₀ relationship breaks down, as had been seen in Figure4. There is little change in r₀ with

log₁₀(M∗/M) Mean log₁₀(M∗/M) r0/h⁻¹Mpc z= 0.8, 41.72 < log10(LHα/erg s⁻¹)< 42.42

8.8 − 9.2 9.02 3.2^+1.2_−0.9

9.0 − 9.4 9.22 2.8^+0.8_−0.6

9.2 − 9.6 9.42 3.1^+0.5_−0.4

9.4 − 9.8 9.61 3.2^+0.5_−0.4

9.6 − 10.0 9.80 3.3^+0.5_−0.4

9.8 − 10.2 10.00 3.2^+0.5_−0.4

10.0 − 10.4 10.19 2.9^+0.4_−0.4

10.2 − 10.6 10.39 3.0^+0.5_−0.4

10.4 − 10.8 10.58 5.3^+0.6_−0.6

10.6 − 11.0 10.76 6.0^+0.9_−0.7

10.8 − 11.2 10.95 5.5^+1.3_−1.0

11.0 − 11.4 11.13 10.6^+3.1_−2.6

z= 1.47, 42.16 < log10(LHα/erg s⁻¹)< 42.86

8.9 − 9.5 9.28 6.8^+4.4_−2.9

9.2 − 9.8 9.55 4.4^+2.8_−1.8

9.5 − 10.1 9.82 3.9^+0.9_−0.7

9.8 − 10.4 10.11 4.1^+0.9_−0.7

10.1 − 10.7 10.38 5.0^+1.0_−0.9

10.4 − 11.0 10.67 6.8^+1.1_−0.9

z= 2.23, 42.47 < log10(LHα/erg s⁻¹)< 43.17

9.3 − 9.7 9.54 8.4^+2.1_−1.8

9.5 − 9.9 9.72 5.2^+1.8_−1.3

9.7 − 10.1 9.93 5.0^+1.4_−1.0

9.9 − 10.3 10.10 4.6^+1.0_−0.9

10.1 − 10.5 10.28 5.3^+1.6_−1.2

10.3 − 10.7 10.49 6.6^+1.8_−1.3

10.5 − 10.9 10.68 7.7^+1.9_−1.4

10.7 − 11.1 10.89 9.6^+1.8_−1.6

10.9 − 11.3 11.07 11.8^+2.4_−2.2

Table 2. Clustering strength, r0, for stellar mass-binned samples of HiZELS galaxies at z= 0.8, 1.47, and 2.23.

stellar mass at fixed L_Hα(if anything, r₀increases slightly as we probe to lower stellar mass at higher L_Hα, where we are probing star-formation rates well above the main sequence).

Next, we show projections of this plot for the z = 0.8 data, and for the smaller samples at z = 1.47 and z = 2.23.

We divide our galaxies at each redshift slice into two stel- lar mass bins, and bin further by L_Hα. We construct two- point correlation functions and obtain correlation strengths for these subsamples. The results are shown in Figure6. We find that the increase in clustering strength with Hα lumi- nosity holds for both stellar mass bins. The trends of the two stellar mass bins are almost indistinguishable. Only the most extremely luminous galaxies at z= 0.8 (LHα> 10^42.2) show any departure from this, and, as found bySobral et al.

(2016), HiZELS samples at these luminosities suffer from sig- nificant AGN contamination.

We also divide our galaxies at each redshift slice into two L_Hα bins, and bin further by stellar mass. The results are shown in Figure 7. Given the size of the sample, our results are clearest at z= 0.8. Here, we find that at all stel- lar masses, the higher luminosity galaxies are more strongly clustered than low luminosity galaxies at the same stellar mass, but this difference is most significant at low stel- lar masses. The data at z = 0.8 (top panel of Figure 4) clearly shows that below stellar masses of M∗ ∼ 10¹⁰M,

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Figure 5. r0in the stellar mass - LHαplane at z= 0.8, constructed using ∼ 500 overlapping (non-independent) subsamples and plot- ted using a smoothed linear interpolation. We overplot the main sequence derived by Speagle et al. (2014) at this redshift as a solid line, with the dashed lines showing the standard deviation.

Clustering strength increases broadly monotonically with LHαat all stellar masses. At high stellar masses M∗& 2 × 10¹⁰M, r0in- creases with stellar mass. We also find large r0values for highly star-forming low stellar mass galaxies that are located well above the main sequence.

HiZELS galaxies have a fairly flat r₀-M∗ relation. At these stellar masses, the higher luminosity subsample displays much stronger clustering than the lower luminosity subsam- ple, with r₀ ∼ 6 − 7h⁻¹Mpc (M_eff ∼ 10¹³M), compared to r₀ ∼ 3 − 4h⁻¹Mpc (M_eff ∼ 10^12.4M). There is even a slight increase in clustering strength towards low masses for the higher luminosity subsample. We find similar trends for our second largest sample, at z= 2.23.

Together, our results present clear evidence for a de- pendence of star-formation activity of low-mass galaxies on environment. For these galaxies, Hα luminosity is a better predictor of clustering strength than stellar mass. As men- tioned in the Introduction, the key difference between this work and many studies of galaxy clustering that use mass- selected samples is the clean, L_Hα-selected sample of star- forming galaxies yielded by our survey. In order to satisfy the HiZELS Hα flux limit, low stellar mass galaxies must lie significantly above the main sequence. One physical in- terpretation of this result is that these galaxies are highly star-forming centrals, which will soon form more stellar mass to put them on the main stellar mass - halo mass relation.

Alternatively, we could be observing an increasing contribu- tion of starbursting satellite galaxies (or galaxies that are infalling on to a massive halo and will soon become satel- lites) at low stellar masses.

4.4 Comparison of star-forming galaxies to mass-selected samples

Here, we compare the clustering of our Hα-selected samples to mass-limited samples.Hatfield et al.(2016) measure the

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Figure 6. Clustering strength as a function of LHαfor HiZELS galaxies split into two stellar mass bins at each redshift. The calculated r0values of the two mass-binned samples are consistent at fixed mass, with the possible exception of the very highest luminosities at z= 0.8. This implies that the Hα luminosity is the physical property most strongly correlated with clustering strength for our HiZELS galaxies.

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Figure 7. Clustering strength as a function of stellar mass for HiZELS galaxies split into two Hα luminosity bins at each redshift. Both high- and low-luminosity massive galaxies are more strongly clustered than their less massive counterparts. Higher Hα luminosity galaxies tend to be more strongly clustered than less luminous galaxies at fixed mass. This is clear for the two largest samples, at z= 0.8 and z= 2.23. The offset in r0between the two luminosity bins is particularly large at low stellar masses, suggesting that low-mass galaxies with high luminosities have environmentally triggered star formation.

clustering of mass-limited galaxy samples from the VIDEO survey at a very similar redshift to our z = 0.8 sample, at 0.75 < z < 1.00 with median redshift z= 0.88.¹ Their selec- tion is based on an apparent AB magnitude limit K_S< 23.5.

Our observations probe slightly deeper, reaching down to K ∼25, but the majority of our sources also satisfy K < 23.5.

1 Note that inHatfield et al. (2016), r0 is not derived from a power-law fit as in this work. Instead, r0is defined as the radius at which the best-fitting spatial correlation function equals unity.

The important difference between our samples is the Hα flux limit of our sample. Whereas we are probing mainly the star-forming population, a substantial proportion of the Hatfield et al.(2016) sample will comprise less highly star- forming and passive galaxies. We characterize the clustering of HiZELS emitters down to the same stellar mass limits as Hatfield et al. (2016), using no luminosity cuts other than the source selection criteria described in Section2.1. The re- sults, shown in the left-hand panel of Figure8, are strikingly different. At identical stellar mass limits, HiZELS r₀ values

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Figure 8. Left: r0as a function of stellar mass lower limit, for HiZELS Hα-selected galaxies and mass-selected galaxies fromHatfield et al.

(2016). At fixed stellar mass limit, the star-forming galaxies display significantly lower r0values, with the difference only decreasing at the highest stellar mass limits. Right: Comparison of whole-sample r0values at different redshifts. There are clear differences in derived r0due to sample selection. In general, samples of passive galaxies (red points) and mass-selected samples (purple points) tend to be more highly clustered than samples of star-forming galaxies at the same redshift (blue points).

are approximately half of the VIDEO mass-selected sample r₀ values, with this difference only decreasing at the highest stellar masses. This shows that, at fixed stellar mass, star- forming galaxies are markedly less strongly clustered than the galaxy population as a whole. Note that for the lowest two stellar mass bins ofHatfield et al.(2016), the K_S< 23.5 selection may mean that only the reddest (and most passive, thus often most clustered) galaxies are included in the anal- ysis, possibly biasing the points upwards relative to a fully mass-selected sample.

We now compare the clustering of our large samples of star-forming galaxies at the three HiZELS redshifts, z= 0.8, z= 1.47, z = 2.23, to other clustering measurements in the literature, to see whether these stark differences between differently selected samples persist at other redshifts. The right-hand panel of Figure8shows the results. We find that samples of passive galaxies and mass-selected samples tend to be more highly clustered than samples of star-forming galaxies at the same redshift, to at least z ∼ 2.

Those results form a parallel story to that already pre- sented here. While we have studied the clustering of star- forming galaxies and shown that more highly star-forming galaxies are more strongly clustered than their less star- forming counterparts at fixed stellar mass, we show here that passive galaxies are more strongly clustered than star- forming galaxies at fixed mass. How do these two apparently contradictory results fit together?Sobral et al.(2011) show that, at fixed stellar mass for M∗< 10^10.6M, the mean star- formation rate of HiZELS galaxies increases strongly with environmental overdensity (Σ_c) across almost the full range of overdensities probed (2 < Σ_c < 30), which included field galaxies and small groups. This is consistent with the main part of our study: the clustering strength of the most highly star-forming galaxies is largest. Janowiecki et al. (2017) study the atomic hydrogen gas fraction of field and small

group galaxies, finding that low-mass (M∗ ≤ 10^10.2M) galaxies in the centres of groups have gas fractions ∼ 0.3 dex higher than those in the field at fixed stellar mass. They con- clude that the higher star-formation activity of these galax- ies is driven by their higher gas availability. Sobral et al.

(2011) also use the underlying photometric sample to esti- mate the star-forming fraction for HiZELS galaxies as func- tion of overdensity. Here, the trends are different. The star- forming fraction increases slowly in the range 2 < Σ_c < 10, but displays a sharp fall above these densities, falling to be- low 15% in the richest clusters. This is entirely consistent with our results: the mass-selected samples ofHatfield et al.

(2016) display higher clustering strengths because they are dominated by passive galaxies in richer environments, which are not detected by the HiZELS survey due to its Hα flux selection. This interpretation, driven by the exclusion of en- vironmentally quenched satellites from our HiZELS samples, is in line with both the low satellite fractions found in C17, and the low M_eff values for HiZELS galaxies in general.

4.5 The stellar mass-halo mass relation

The stellar mass to halo mass ratio (SHMR) is defined as the total stellar mass within a halo divided by the dark matter halo mass. It reflects the relative star formation and satellite galaxy accretion of a halo, compared to its dark matter ac- cretion history, and is effectively a measure of the efficiency of the conversion of baryons into stars. The least massive dark matter haloes build stellar mass inefficiently due to supernova feedback, resulting in low M∗/M_halofractions. Ef- ficiency appears to increase towards higher halo mass, up to M_halo∼ 10¹²M. A consensus has emerged that haloes of this mass are most efficient at forming stars, with substantial de- crease in efficiency above this halo mass (e.g.Behroozi et al.

2013; Moster et al. 2013), which is associated with AGN

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Figure 9. Left: The stellar mass - halo mass relation fromMoster et al.(2013), with whole HiZELS samples at each redshift overplotted.

We use the effective halo mass estimated via the HOD fitting to the whole HiZELS samples at each redshift (see C17). Error bars on the y-axis represent the 1σ uncertainty derived from the MCMC posterior distribution, combined in quadrature with the typical errors on the stellar mass measurements (0.23, 0.24, and 0.26 dex for z= 0.8, 1.47 and 2.23 respectively). At all three redshifts, HiZELS galaxies occupy a region at the peak of the SMHR, where conversion of baryons into stellar mass is at a maximum. Right: The stellar mass - halo mass relation fromMoster et al.(2013) as a function of stellar mass, with mass-binned HiZELS data from the z= 0.8 sample within the range 41.72 < LHα< 42.42 overplotted. While high-mass emitters lie on the relation predicted byMoster et al.(2013), the lowest mass Hα emitters lie significantly below it, which indicates that these galaxies are living in more massive haloes than would be expected for central galaxies of their stellar masses.

feedback.Birrer et al. (2014) find that the reduced stellar- to-halo mass ratio can be accounted for at high halo masses by the quenching of massive galaxies at around M^∗, the knee of the stellar mass function. There is little evidence for red- shift evolution in the peak of the SHMR. Here, we review one approach to modelling the SHMR, and compare our mea- surements to predictions.

Moster et al. (2013) follow Moster et al. (2010) in adopting a double power-law parametrization for the SMHR.

The four free parameters are fitted using populations of dark matter haloes and galaxies at redshifts from z = 0 to z = 4, specifically dark matter halo populations drawn from the Millennium and Millennium-II Simula- tions (Springel et al. 2005;Boylan-Kolchin et al. 2009) and galaxy populations fromLi & White(2009) at low redshifts and P´erez-Gonz´alez et al. (2008) and Santini et al. (2012) at high redshifts. At each redshift,Moster et al.(2013) ini- tiate an SMHR with a given set of parameters, and use this to simulate the stellar masses of galaxies within the dark matter haloes they draw from the N-body simulation at the same redshift. They then compare the stellar masses of their simulated galaxies to the observed stellar mass function, and assign the modelled SMHR a likelihood. They thus optimize the parameters of the SMHR at each redshift. By including observational errors on high-redshift stellar masses, they are able to derive models that agree well with observed stellar mass functions.

Behroozi et al.(2010) show (using another stellar mass- limited approach) that there is little difference between the SHMRs at low halo masses (M_halo< 10¹²M) derived when considering the total stellar mass within the halo or just that

of the central galaxy. Given that we argued in C17 that the HiZELS samples are dominated by central galaxies, we use the stellar mass of HiZELS galaxies as a proxy for total stel- lar mass in the halo. We then compare our estimates of dark matter halo mass for HiZELS galaxies to the predictions of Moster et al.(2013). We take the same samples of galaxies within large L_Hα/L^∗

Hαbins at each of the three redshifts, as in C17. We estimate average SED masses as in Section2.2, and use the effective halo masses derived from HOD fitting (see Section3.3) to place these samples on to the SHMR.

The left-hand panel of Figure 9 shows that our data are in excellent agreement with the predictions ofMoster et al.

(2013). At all three redshifts, HiZELS galaxies occupy a re- gion at the peak of the SMHR. They reside in haloes that are able to support maximum conversion of baryons into stellar mass.

Nevertheless, these global averages include galaxies spread over > 2 dex in stellar mass, so are not necessarily representative of all HiZELS galaxies. To investigate this, in the right-hand panel of Figure9we place mass-selected sub- samples of our z= 0.8 data on to the same relation. When we calculate the SMHR from the mean stellar mass and derived effective halo mass for each subsample, samples of galaxies with M∗ > 10¹⁰M lie approximately on the Moster et al.

(2013) relation. However, at low stellar masses, our samples lie significantly below this modelled relation. As discussed in Section4.3, our low-mass galaxies reside in particularly high-mass haloes for central galaxies of their stellar mass.

One possible interpretation of this is that it could be in- dicative of a substantial amount of stellar mass contained in galaxies that are undetectable by HiZELS within the same